Simplify 3x cube root of x^8y+x^2 cube root of x^5y

$3 x \sqrt[3]{x^{8} y} + x^{2} \sqrt[3]{x^{5} y}$

Simplify each term.

Rewrite $x^{8} y$ as ${(x^{2})}^{3} (x^{2} y)$ .

Factor out $x^{6}$ .

$3 x \sqrt[3]{x^{6} x^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$3 x \sqrt[3]{{(x^{2})}^{3} x^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Add parentheses.

$3 x \sqrt[3]{{(x^{2})}^{3} (x^{2} y)} + x^{2} \sqrt[3]{x^{5} y}$

Pull terms out from under the radical.

$3 x (x^{2} \sqrt[3]{x^{2} y}) + x^{2} \sqrt[3]{x^{5} y}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$3 (x^{2} x) \sqrt[3]{x^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$3 (x^{2} x^{1}) \sqrt[3]{x^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{2 + 1} \sqrt[3]{x^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Add $2$ and $1$ .

$3 x^{3} \sqrt[3]{x^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Rewrite $x^{5} y$ as $x^{3} (x^{2} y)$ .

Factor out $x^{3}$ .

$3 x^{3} \sqrt[3]{x^{2} y} + x^{2} \sqrt[3]{x^{3} x^{2} y}$

Add parentheses.

$3 x^{3} \sqrt[3]{x^{2} y} + x^{2} \sqrt[3]{x^{3} (x^{2} y)}$

Pull terms out from under the radical.

$3 x^{3} \sqrt[3]{x^{2} y} + x^{2} (x \sqrt[3]{x^{2} y})$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$3 x^{3} \sqrt[3]{x^{2} y} + x \cdot x^{2} \sqrt[3]{x^{2} y}$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$3 x^{3} \sqrt[3]{x^{2} y} + x^{1} x^{2} \sqrt[3]{x^{2} y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{3} \sqrt[3]{x^{2} y} + x^{1 + 2} \sqrt[3]{x^{2} y}$

Add $1$ and $2$ .

$3 x^{3} \sqrt[3]{x^{2} y} + x^{3} \sqrt[3]{x^{2} y}$

Add $3 x^{3} \sqrt[3]{x^{2} y}$ and $x^{3} \sqrt[3]{x^{2} y}$ .

$4 x^{3} \sqrt[3]{x^{2} y}$